In the fully observed setting, estimates for \((A,B)\)  can be obtained by solving ordinary least-squares (OLS) optimization problems. A series of recent papers [1]}, [2]}, [3]}, [4]}, [5]} have derived non-asymptotic guarantees for ordinary least-squares (OLS) estimators. In the case of partially observed systems, which is conceptually more complicated than the fully observed case, OLS optimization can be used to estimate the Markov parameters associated with (REF ) from which the Ho-Kalman algorithm [6]} can be employed to estimate the system parameters \((A,B,C,D)\) . The process of obtaining estimates of the system matrices from the Markov parameters is referred to as system realization which is the main focus of this paper. Using this framework, the authors of [3]}, [8]}, [9]}, [10]}, [11]}, [12]} have derived non-asymptotic estimation error bounds for the system parameters which decay at a rate \(O( \frac{1}{\sqrt{N}})\) . Note that these papers make different assumptions about the stability, system order, and the number of required trajectories to excite the unknown system.
